Question

twice the sum of a number and 8 is equal to three times the difference of the number and 6

Answer 1

It can be easier to figure this out if you break everything down. First start by declaring a variable in place of "a number". We can use x.
Then we can move on and look at the left side of the equal sign, "twice the sum of a number and 8".
The sum of a number and 8 can be written as x + 8. Twice the sum is simply multiplying by 2. So we can write that as 2(x+8).
Next we'll look at the other side of the equal sign. "three times the difference of the number and 6". The difference of a number and 6 can be written as x-6. Three times the difference would be 3(x-6).
Then you combine everything together.
2(x+8) = 3(x-6).
Solve.